subjected to fault offset behaviour of segmental pipeline
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Behaviour of segmental pipeline protective vaultssubjected to fault offsetChi-Chin Tsaia, Philip Meymandb, Ethan Dawsonb & Stephanie A. Wongc
a Department of Civil Engineering, National Chung Hsing University, 250 Kuokuang Road,Taichung, Taiwanb URS Corporation, 1333 Broadway, Suite 800, Oakland, CA 94612, USAc San Francisco Public Utilities Commission, 525 Golden Gate Avenue, 11th Floor, SanFrancisco, CA 94102, USAPublished online: 08 Oct 2014.
To cite this article: Chi-Chin Tsai, Philip Meymand, Ethan Dawson & Stephanie A. Wong (2014): Behaviour of segmentalpipeline protective vaults subjected to fault offset, Structure and Infrastructure Engineering: Maintenance, Management,Life-Cycle Design and Performance, DOI: 10.1080/15732479.2014.964733
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Behaviour of segmental pipeline protective vaults subjected to fault offset
Chi-Chin Tsaia*, Philip Meymandb1, Ethan Dawsonb2 and Stephanie A. Wongc3
aDepartment of Civil Engineering, National Chung Hsing University, 250 Kuokuang Road, Taichung, Taiwan; bURS Corporation,1333 Broadway, Suite 800, Oakland, CA 94612, USA; cSan Francisco Public Utilities Commission, 525 Golden Gate Avenue, 11th Floor,
San Francisco, CA 94102, USA
(Received 15 February 2014; final version received 28 June 2014; accepted 20 July 2014)
The San Francisco Public Utilities Commission is currently undertaking a seismic upgrade of Bay Division Pipelines(BDPLs) Nos. 3 and 4 located in Fremont, California. To improve the reliability of the pipelines at a crossing of the HaywardFault, a new pipeline (BDPL No. 3X) will be constructed in a segmental reinforced concrete vault with flexible connectionjoints that can accommodate lateral offsets and compressive deformations during a significant fault rupture. FLAC 3D finitedifference analysis was performed to enhance the understanding of the soil–structure interaction behaviour of this specialdesign. The analysis focused on the behaviour of the segmental concrete vault when subjected to up to 2.0m (6.5 ft) lateralfault movement. The effects of fault intersection angle, fault location, soil strength, backfill type and connection joint size onthe performance of the segmental concrete vault were also evaluated. Numerical results show that the movement of the vaultdeveloped gradually without sudden or concentrated deformation in response to the increasing fault displacement. Hence,the articulated vault design can withstand significant lateral offset and compressive deformation during fault rupture throughthe relative slip and rotation of the flexible connection joints.
Keywords: segmental vaults; pipelines; seismic design; numerical simulation; soil–structure interaction; fault offset
1. Introduction
The San Francisco Public Utilities Commission’s (SFPUC)
Hetch Hetchy Regional Water System supplies an average
of 260 million gallons of drinking water to 2.5 million
people in the San Francisco Bay Area each day. The system
was built in the early 1900s and carries water 267 km across
California from the Hetch Hetchy Reservoir in Yosemite
National Park to the Bay Area through a gravity-driven
network of pipelines, tunnels, pump stations, dams,
reservoirs and tanks as shown in Figure 1. Beginning in
the city of Fremont, the water is conveyed in four pipelines,
namely, BayDivision Pipelines (BDPLs)Nos. 1–4. BDPLs
1 and 2 carry the water westward across the San Francisco
Bay, whereas BDPLs 3 and 4 turn southward and continue
around the southern portion of the San Francisco Bay
through Santa Clara and San Mateo counties.
BDPLs 3 and 4 are vital components of the SFPUC’s
water transmission system. One of the most vulnerable
areas of the system is in the city of Fremont, where BDPLs
3 and 4 cross the Hayward Fault (Figure 1), an active fault
with a significant probability of a large ground-rupturing
earthquake. The most serious damage to underground
pipelines during an earthquake has long been recognised
as caused by permanent ground deformation (PGD)
(Hamada & O’Rourke, 1992; O’Rourke, 1998; O’Rourke
& Liu, 1999). One of the prominent PGD hazards is due to
fault rupture. Therefore, a new BDPL 3X is designed to
replace the existing BDPL 3, and accommodate the design
fault displacement. The new pipeline is designed to
withstand a major earthquake and protect the pipe. The
design entails enclosing BDPL 3X in a segmental
reinforced concrete vault with special joints that can
accommodate lateral offset and compressive deformation
during fault rupture; the rotation and compression of the
pipeline inside the vault are accommodated by ball joints
and slip joints, respectively. However, the feasibility of
this BDPL 3X system to accommodate fault rupture
requires a detailed technical evaluation because it involves
a complex mechanism of soil–structure interaction.
Different approaches have been applied to explore the
soil–structure interaction behaviour of pipeline response
to fault rupture. Trifonov and Cherniy (2012) presented an
analytical model of the stress–strain analysis of buried
steel pipelines subjected to active fault displacements.
Simplified finite element methods (Cocchetti, di Prisco,
& Galli., 2008; Joshi, Prashant, Deb, & Jain, 2011), which
utilised beam elements for the pipeline and discrete
nonlinear springs for the soil, have been commonly
adopted to analyse buried pipelines subjected to fault
motion in engineering practice. The complex soil–
pipeline system can be rigorously modelled with 3D finite
elements (e.g. Vazouras, Karamanos, & Dakoulas, 2010;
q 2014 San Francisco Public Utilities Commission
*Corresponding author. Email: tsaicc@nchu.edu.tw
Structure and Infrastructure Engineering, 2014
http://dx.doi.org/10.1080/15732479.2014.964733
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Xie et al., 2013) to account for large strains and
displacements, nonlinear material behaviour and special
conditions of contact and friction on the soil–pipe
interface. Large-scale (Kim et al., 2009; O’Rourke &
Bonneau, 2007) and centrifuge tests (Ha et al., 2008;
Moradi, Rojhani, Galandarzadeh, & Takada, 2013;
O’Rourke, Gadicherla, & Abdoun, 2005) have also been
employed to simulate the pipeline response to ground
rupture and obtain the soil pressure distributions and
lateral reaction of pipelines subjected to fault movement.
However, most of these studies except for Kim et al.
(2009) were conducted for continuous pipeline systems in
response to fault ruptures. A segmented system, such as
BDPL 3X, has been investigated.
Numerical analyses were performed in this study using
the FLAC 3D finite difference model to better understand
the behaviour of the BDPL 3X segmented vault subjected
to fault rupture. In contrast to previous studies that focused
on continuous pipelines, the present study emphasised the
behaviour of segmented vaults that consist of reinforced
concrete trapezoidal boxes with gaps between each
segment. Different models were applied to explore the
effect of fault position, backfill properties, native soil
properties and connection joint sizes on the performance
of the segmented vault.
2. Fault crossing design detail
2.1 Design basis
BDPL 3X crosses the Hayward Fault at approximately 478(William Lettis and Associates [WLA], 2008), such that a
right lateral strike-slip movement of the fault will cause
compression in the pipeline. Strain limits are typically
utilised to guard against localised wrinkling or tensile
fracture of the pipeline induced by PGD (American Lifelines
Alliance [ALA], 2001a). The latest American Society of
Civil Engineers (ASCE) Manual of Practice 119 for Buried
Steel Pipes (ASCE, 2009) specifies the maximum allowable
strain for compression equal to the minimum of [0.01, 0.4t/
D ], in which t/D is thickness-to-diameter ratio of pipeline.
Accordingly, steel pipes may sometimes be able to
accommodate fault crossing displacements up to a few feet
(ALA, 2001b) depending on compression strain that is
dependent on fault-cross angle, fault deformation, surround-
ing soil strength, soil stiffness and pipeline properties.
Vazouras et al. (2010) recently presenteddesigndiagrams
that depict critical fault displacement and the corresponding
critical strain versus the pipe diameter-to-thickness ratio for
various soil and pipeline parameters. According to Vazouras
et al. (2010), given the site condition and the pipe properties
of BDPL 3X, critical fault displacement is estimated to be
approximately 2 ft (0.6m), which is far below the design
displacement of 6.5 ft (2.0m). A special design solution is
therefore required to prevent pipe failure.
2.2 Protective vault
To accommodate strike-slip offset in compression and
protect the pipeline from wrinkling, the pipeline will be
constructed in a protective segmental concrete vault at the
fault crossing. The design concept is shown in Figure 2.
Fault deformation or fault-induced compression strain can
be accommodated by the relative slip and rotation of the
connection joints. The length of the protective vault is
,91.4m (300 ft), and the width, height and length of the
reinforced concrete segments (boxes) are approximately
6.1m (20 ft). The connection joints with 15-cm (6 in.)
Figure 1. Hetch Hetchy regional water system and fault systems in the San Francisco Bay area.
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spacing between concrete segments are oriented at 458withrespect to the longitudinal axis of the vault; thus, they are
approximately parallel to the strike of the fault. Figure 2
shows the ball joints installed in the pipeline to allow for
rotation in response to a fault offset. A slip joint is installed
to accommodate compression in the pipeline. The pipeline
is supported by sliding and guided supports to allow and
further control the horizontal movement. The protected
vault segments are cast in place on unreinforced mud slabs.
2.3 Shoring system
The newly designed BDPL 3X will be constructed by top–
down construction method and will carry a series of
temporary bridges to carry traffic acrossMissionBoulevard
and the northbound Interstate 680 on-ramp north of
Mission Boulevard. The depth of excavation will be
approximately 9m. The excavation shoring system is
designed as two parallel cast-in-drilled-hole (CIDH) secant
pile walls that consist of a series of overlapping primary and
secondary piles. The short primary piles are constructed
with lean concrete, and the long secondary piles are
constructed with reinforcing cages and structural concrete.
The CIDH wall will remain in place after the vault is
constructed. A typical completed section after the upgrade,
as shown in Figure 3, includes the protective vault, bottom
mud slab, secant pile wall, backfill between the vault and
secant pile wall and compacted pavement and subgrade.
The presence of the CIDH wall and other components can
also affect the vault response during fault movement.
3. Numerical analysis
Three-dimensional (3D) numerical analyses of the soil–
structure interaction were performed to gain insight into the
behaviour of BDPL 3X in response to a fault rupture.
A critical aspect of the system is the relativemovement of the
concrete vault segments to accommodate lateral offset and
compressive deformation during fault rupture. Understand-
ing the relativemovement of the segmentswith respect to one
another and the effects on the enclosed pipeline (i.e. rattle
space, the distance between the pipeline and the vault wall) is
a key component of the investigation process. Therefore,
analyses were performed to focus on the behaviour of the
segmental concrete vault. The entire pipeline and its supports
were not included in the numerical model.
Figure 2. Design solution of BDPL 3X at the Hayward Fault crossing. (a) Section view along the pipeline longitudinal direction.(b) Plan view.
Structure and Infrastructure Engineering 3
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3.1 FLAC 3D model
The FLAC 3D model captures the primary design features
(Figure 3), including the vaults, secant pile wall (primary
and secondary piles), bottom mud slab, native soil, backfill
and compacted fill (pavement subgrade), and has a total of
50,000 elements. Figure 4 shows the overall view of the
model mesh. Fine meshes were generated near the fault
(centre of the model) and pipeline alignment.
To accommodate a 458 vault angle and a 458–508 faultintersection angle, all meshes were generated in a
‘parallelogram’ shape by using the selected angle with
respect to the pipeline transverse direction. The purpose of
this setup is not only for convenience in mesh generation
but also to avoid significant distortion in the elements when
the model encounters a large fault displacement. Another
feature of the model (as shown in Figure 5) includes the
connection joints (gaps) between vaults, which also impose
challenges in mesh generation and computation stability
owing to their small size compared with the entire model.
Furthermore, interface elements were installed on all
surrounding vaults to allow for relative movements
between the vault segments (boxes) and the surrounding
elements and to monitor the contact forces if the boxes
collide. The nine vault segments (boxes) closest to the fault
rupture plane were modelled to understand the box
reactions relative to the fault trace.
The different model types and the corresponding
properties assigned to the different materials are listed in
Table 1. The segmented vaults were modelled as rigid
boxes because the primary purpose of the simulation is to
understand the global behaviour of the vaults. The
connection joints between the segment vaults were
reproduced by a null model that induces zero stiffness.
The secant pile walls that consist of a series of primary and
secondary piles were modelled by a composite of solid and
pile elements. Short primary piles without reinforcement
were built with solid elements with a size that produces
equivalent bending stiffness. A strain softening model was
adopted to capture the weakening behaviour of the primary
pile (i.e. a fault could rupture through). Meanwhile, long
reinforced piles were simulated with a composite of
structure pile and solid elements with a size that produces
equivalent bending stiffness. Mud slabs without reinforce-
ment were also established by the strain softening model
similar to that of the primary pile of the secant pile wall.
Geofoam backfill, which exhibits strain hardening
behaviour, was modelled by a double-yield model with
calibrated model parameters.
Figure 3. Cross section along the pipeline transverse direction.
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3.2 Boundary condition and analysis procedure
Prior to the fault rupture simulation, the gravity load was
applied first so that the model could achieve equilibrium
condition. At this stage, the bottom of the model was
designated with fixed boundary conditions (translations of
three directions were prevented), whereas the four sides
were fixed in the horizontal direction but remained free in
the vertical direction. No staged construction in the
excavation, such as secant pile wall installation and vault
placement, was modelled. In the second stage, the
boundaries on the four sides and bottom of the model
were fixed in the three directions and then subjected to
displacements similar to those of a rigid shear box
movement to mimic a fault rupture.
The models were simulated to impose a straight, planar
(knife edge) ground rupture without dispersion of the fault
trace to set an upper bound for the deformation effects.
Half of the design fault displacements (1.0m) were
applied incrementally at each side of the fault plane in
opposite directions rather than impose the entire design
fault displacement (2.0m) on one side so that the model
could attain equilibrium faster. The analysis was
conducted under a quasi-static condition, which applies
fault offset gradually to allow the model to reach
equilibrium at each incremental fault movement.
3.3 Analysis output
When the fault displacements were applied, the model
continuously monitored the movement of the boxes and
the forces that act on the boxes induced by the fault
movement. Figure 6 shows the notation of output data
related to box mobility, including the box rotations along
the longitudinal, transverse and vertical directions, the two
Figure 4. FLAC 3D model and 3D view.
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sides of the box offset (east and west) relative to the
adjacent box and the gap spacing. The forces that act on
the boxes, including normal forces acting on the two sides
of the box and box-to-box contact forces, were also
monitored.
3.4 Analysis cases
Ten cases, presented in Table 2, were analysed. The
analysis of these cases was performed in consideration of
the factors that can affect box movement, including fault
location, fault angle, native soil strength, backfill type and
connection joint size. Case 1 was utilised to evaluate the
effect of fault location on box movement. The fault plane
was made to pass through the centre, the quarter point and
the edge of the central box. Case 1-A, which utilised the
best estimated model parameters (478 of the fault angle,
lower bound of the soil strength and sand backfill) was
defined as the baseline model. Case 2 was utilised to
evaluate the effect of the fault angles on box movement.
According to the range of fault angles reported by WLA
(2008), the analysed fault angles were set to 458 and 508 inCases 2-A and 2-B, respectively.
Case 3 was utilised to evaluate the effect of variation in
native soil strength (medium to very stiff clays as listed
in Table 3 according to URS Corporation [2010]) and
backfill type on box movement. In Case 3-A, the upper
bound native soil strength was adopted; the other variables
were kept similar to those of the baseline model. In Case 3-
B, a Geofoam-type backfill was utilised; however, the
other variables were kept similar to those of the baseline
model. Case 4 was utilised to evaluate the impact of
Table 1. Models and parameters utilised in FLAC analysis.
Material Model Parameter
Native soil (lower bound) Mohr–Coulomb Su (Table 3), E ¼ 250 Sua, n ¼ 0.5, g ¼ 19.7 kN/m3
Native soil (upper bound) Mohr–Coulomb Su (Table 3), E ¼ 600 Sub, n ¼ 0.5, g ¼ 19.7 kN/m3
Loose sand backfill Mohr–Coulomb c0 ¼ 0, f ¼ 30, E ¼ 13.8MPa, n ¼ 0.2, g ¼ 18.9 kN/m3
Geofoam backfill Double yield qu ¼ 23.4 kPa, E ¼ 2.39MPa, n ¼ 0.08, g ¼ 0.14 kN/m3
Compacted fill Mohr–Coulomb c0 ¼ 0, f ¼ 36, E ¼ 68.8MPa, n ¼ 0.35, g ¼ 20.4 kN/m3
Box Elastic E ¼ 27,000MPa, n ¼ 0.18, g ¼ 23.6 kN/m3
Slab Strain softening f 0c ¼ 332MPa, E ¼ 8260MPa, n ¼ 0.18, g ¼ 22.8 kN/m3
Primary pile of the secant pile wall Strain softening f 0c ¼ 332MPa, E ¼ 8260MPa, n ¼ 0.18, g ¼ 22.8 kN/m3
Secondary pile of the secant pile wall Beam E ¼ 23,800MPa, n ¼ 0.18, g ¼ 23.6 kN/m3
Gap Null –
a Assuming that OCR ¼ 2 and PI ¼ 50 (Duncan & Buchignani, 1976).b Assuming that OCR ¼ 2 and PI ¼ 30 (Duncan & Buchignani, 1976).
15 cm gap betweenbox and slab segments
Interface elementssurrounding the boxes
Figure 5. Features of the FLAC 3D model: 15-cm gaps and the surrounding interface elements outside the boxes.
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connection joint size on box movement. In addition to
varying the connection joint size from 6 in (15 cm) to 12 in
(30 cm), the other analysed variables were selected based
on the results of Cases 1–3 to consider the most
unfavourable condition.
4. Model verification with a large-scale test
The modelling technique described previously was
verified against physical model data obtained from a
large-scale test. The 1/10 scale models of the protective
concrete enclosures were established with the Large-Scale
Lifelines Testing Facility at Cornell University, which is a
part of the Network for Earthquake Engineering Research.
Similar to the purpose of FLAC analysis, the scale model
tests also aim to validate the effect of fault location and
back fill type on box movement. However, unlike FLAC
analysis which considered a range of fault angles, the fault
angles of the Cornell scale model tests were fixed at 508.In addition, the constraints of the cover plate between
connection joints were varied in these tests, unlike the
FLAC analysis. The details of the Cornell model test can
be obtained from Cornell University (2009).
FLAC Case 4-C and Cornell Case 1-E, designed for
similar scenarios, were selected for comparison. The
verification focused on the generalised relative displacement
of the boxes caused by fault movement, specifically, the
relative offset and rotation of the boxes. Figure 7 shows the
comparison of FLAC simulation results and the Cornell
model test results. The lateral displacements of the vault
segments shown in Figure 7(d) are relative to a horizontal
line that represents the initial position of the south end vault
before fault rupture. The Cornell test reported the movement
of the centre of box, whereas FLAC reported the movement
of the four corners of the box. It is easier to observe the offset
between two adjacent boxes. The FLAC simulation of box
response agrees favourably with that of the Cornell model
test in terms of rotations and lateral displacements.
5. Soil–structure interaction behaviour
The BDPL 3X system will interact with the surrounding
soil (referred to as soil–structure interaction) and cause
the ground rupture to behave differently. Figure 8 shows
the displacement contour at a 2.0-m fault displacement of
Case 4-A. In the bottom view where only the soil is shown,
Offset
Offset
Gap dist.
Gap dist.
Normal Force
Normal Force
Rotation
Contact Force
x
y
z
West East
Figure 6. Notation of the output parameters.
Table 2. FLAC analysis cases.
Case Fault location Fault angle (8) Box angle (8) Joint size (cm) Soil strength Backfill Note
1-A Centre of the box 47 45 15 Lower bound Sand Baseline model1-B Quarter of the box 47 45 15 Lower bound Sand1-C Edge of the box 47 45 15 Lower bound Sand2-A Centre of the box 45 45 15 Lower bound Sand2-B Centre of the box 50 45 15 Lower bound Sand3-A Centre of the box 47 45 15 Upper bound Sand3-B Centre of the box 47 45 15 Lower bound Geofoam4-A Quarter of the box 50 45 15 Upper bound Geofoam4-B Quarter of the box 50 45 22.5 Upper bound Geofoam4-C Quarter of the box 50 45 30 Upper bound Geofoam
Table 3. Soil strength profile (URS, 2010).
Depth (m) Lower bound Su (kPa) Upper bound Su (kPa)
0–9 140–40 360–2759–12 41 27512–21 40–230 275–36021–33 40 360
Note: Su linearly changes with depth if a range of Su is presented
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a knife-edge type of fault displacement is clearly observed
because the models were simulated by introducing a
straight planar ground rupture. The top view, however,
shows that the fault movement spreads out because of the
interference of the BDPL 3X system. Moreover, the cut
section view near the fault plane indicates that different
displacements of the adjacent native soil are developed.
The soil deformed upon contact with the system in
opposite directions from each side of the fault in response
to the right lateral strike-slip displacement. This condition
typically generates a passive pressure reaction at each side
of the fault as shown in Figure 9. The soil on the other
sides of the vault opposite the passive pressure sides
tended to move away from the concrete segments and thus
created an active pressure zone as shown in Figure 9.
These phenomena are consistent with those in a previous
study on continuous systems (O’Rourke et al., 2008).
However, soil zones (active and passive) in Figure 9
exhibit different apparent sizes on the different sides of the
system. This is because the fault plane was made to pass
through the quarter point of box, which imposes a non-
symmetric condition.
The active pressure or extension zones are confined to
the region bounded by a distance of approximately 1–1.5
segment lengths from either side of the fault. The system
has a limited capability to transfer the bending stresses and
distribute the axial compression induced by the fault offset
because of the weak connection joint between the boxes
opposite the continuous pipeline. Consequently, major soil
structure interaction is encountered within a narrow region.
Figure 10 depicts the plan view of the deformed mesh
6.1m below the ground surface (mid elevation of the box)
–2
–1
0
1
2(a) (b)
(c) (d)
–25–20–15–10–50510152025
Rot
atio
n ab
out l
ongi
tudi
nal
axia
l (de
gree
s)
Distance from fault (m)
CornellFLAC
0
1
2
3
4
5
–25–20–15–10–50510152025
Rot
atio
n ab
out v
ertic
alax
ial (
degr
ees)
Distance from fault (m)
–2
–1
0
1
2
–25–20–15–10–50510152025
Rot
atio
n ab
out t
rans
vers
eax
ial (
degr
ees)
Distance from fault (m)
0
0.5
1
1.5
2
–25–20–15–10–50510152025
Tran
sver
se d
ispl
acem
ent (
m)
Distance from fault (m)
West
East
Figure 7. Comparison of FLAC simulation results and Cornell model test results.
Bottom View
Top View
Pipelinedirection
Faultdirection
Cross Section
0.0m
1.0mInterval=0.15m
Figure 8. 3D view of the displacement contour, Case 4-A.
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after a 2.0-m fault displacement. Some of the observed
general features of the system response are as follows:
. The boxes experienced rotation and lateral move-
ment (offset) as rigid bodies.. Some gaps were closed (i.e. boxes collided) as a
result of box rotation and lateral offset. Partial
connection joint closure occurred as far as one to
two segments from both sides of the fault.. The space between the vault and the secant pile wall
was reduced at one side (points A and A0 where thefault moved toward the vault) and widened at the
other side (points B and B0 where the fault moved
away from the vault).. The fault rupture broke through the secant pile wall
at the location of the unreinforced primary pile.
Consequently, soil displacement propagated
through this weak point and imposed lateral offset
on the segmented vaults at the connection joints.
6. Monitored analysis output
The history of the box mobility subjected to fault offset
can be better understood by continuously monitoring with
FLAC. Figure 11 shows an example of the monitored
data of Case 4-A on box rotation, box offset, gap
distance, side force acting on the box and box-to-box
contact forces corresponding to different fault displace-
ments. The system response can be further characterised
as follows:
1. The boxes experienced rotation. The box rotation
along the vertical axis at the centre box (Box 5)
increased linearly (starting at 0.1m fault offset)
with the fault movement up to 2.78 at a 2.0-m fault
displacement. The two adjacent boxes exhibited
delayed responses (starting at 0.5m fault offset)
and rotated linearly initially up to a 1-m fault offset
before reaching the maximum rotation at the 1.1-m
fault displacement. The boxes also exhibited
rotation along the transverse and longitudinal
axes; however, such rotation was insignificant
compared with the rotation along the vertical axis.
2. The boxes moved laterally. The degree of
translation can be quantified by the offset between
two adjacent boxes as indicated in Figure 6. The
box offset at the centre increased linearly with the
fault movement and reached 1.1m at a 2.0-m fault
displacement. Similar to the rotation response, the
offset mostly occurred near the fault trace.
3. The combined effects of rotation and translation
(both longitudinal and transverse directions) were
reflected in the reduced or opened gap width. In this
case, the gap between Boxes 4 and 5 began to close
at the 0.6-m fault displacement on one side,
whereas the gap on the other side tended to widen.
The gaps between Boxes 3 and 4 and between
Boxes 5 and 6 closed eventually at the 0.9-m and
Figure 10. Plan view of the deformed mesh 6.1m below theground surface (middle elevation of the boxes) at a 2.0-m faultmovement, Case 4-A.
Active zone
Passive zone
Passive zone
Active zone
Figure 9. Plan view of the shear strain contour 6.10m below theground surface at a 2.0-m fault movement, Case 4-A. The circlesindicate the secondary pile location.
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0 0.5 1 1.5 2
0
–1
–2
–3
–4
–5(a)
(c)
(e)
(g)
(b)
(d)
(f)
Fault Displacement (m)
Rot
atio
n A
ngle
(D
egre
e)Rotation about transverse axis
0 0.5 1 1.5 2
0
1
2
3
4
5
Rot
atio
n A
ngle
(D
egre
e)
Rotation about vertical axis
0 0.5 1 1.5 2
0
10
20
30
40
50
60
Fault Displacement (m)
Gap
Wid
th (
cm)
Gap Width
0 0.5 1 1.5 2
0
500
1,000
1,500
2,000
2,500
3,000
3,500
4,000
4,500
Fault Displacement (m)
Nor
mal
forc
e (k
N)
Box to box contact force
0 0.5 1 1.5 2
0
–1
–2
–3
–4
–5
Fault Displacement (m)
Rot
atio
n A
ngle
(D
egre
e)
Rotation about longitudinal axis
0 0.5 1 1.5 2
0
0.5
1
1.5
Fault Displacement (m)
Box
Offs
et (
m)
Box offset
0 0.5 1 1.5 2
0
5,000
10,000
15,000
Fault Displacement (m)
Nor
mal
forc
e (k
N)
Normal force on boxes
Box1Box2Box3Box4Box5Box6Box7Box8Box9
Box1 & Box2Box2 & Box3Box3 & Box4Box4 & Box5Box5 & Box6Box6 & Box7Box7 & Box8Box8 & Box9
Legend of rotationLegend of offset, gap width, and force
East component
West component
Box 1 and Box 2: Between Box1 and Box2
Figure 11. Box response versus fault movement, Case 4-A.
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1.1-m fault displacements, respectively. Right
lateral fault movement with an approximate 458intersection angle imposes a compression mode to
the system and reduce gap width typically.
However, the fault movement also cause the box
rotation, which can increase or decrease gap size on
each side of box depending on the magnitude of box
rotation relative to the adjacent one. The centre box
experienced largest rotation to overcome the
compression and, thus, resulted in gap opening
while the other gaps showed closing.
4. According to items 1–3, box deformation as
indicated by the box rotation, box offset and gap
distance occurred primarily within the central three
boxes near the fault trace.
5. At approximately the 0.5-m fault movement, the
model began to detect the box-to-box contact force,
which is also the moment when the gap closed.
6. The normal stress on the side wall of the boxes
increased with fault displacement. The increase in
stress was due to the passive pressure transmitted to
the backfill material between the box and the secant
pile wall as shown in Figure 9. Unlike box
deformation, however, the increase in stress
occurred primarily at the centre box.
7. Variations in vault response
The variations in fault location, fault angle, material
strength and connection joint size were considered from
Cases 1-A to 4-C and were implemented in the FLAC
model to evaluate the effect of these factors on system
response. Figure 12 shows the final box position under the
2.0-m fault movement. Figure 13 provides a comparison of
the responses of the different cases. As shown in Figure 13,
the forces acting on the box are normalised by the
maximum horizontal passive pressure mobilised by the
native soil. The analysis results are discussed below:
1. Case 1 – Variation in the fault location: The
maximum box rotation about vertical axis occurred
in the case where the fault was forced to rupture at
the quarter point of the box, and the largest box
offsets (i.e. greatest reduction in the rattle space)
were observed with the fault at the edge of the box.
However, the fault movement-induced soil force
was similar regardless of the fault location.
2. Case 2 – Variation in the fault angle: Comparison of
Cases 1-A, 2-A and 2-B indicates that the maximum
box rotation occurred at a fault intersection angle of
508, which is the maximum difference between the
fault and the box angles. The box rotation in this case
was considerably higher than that in the other two
cases; consequently, the gap space closed at the 1.5-
m fault movement. Moreover, the fault movement-
induced soil force in this case was also higher than in
the other two cases.
3. Case 3 – Variation in the materials: In the high
stiffness contrast between the native soil and the
backfill material (e.g. Case 3-A vs. Case 1-A or Case
1-A vs. Case 3-B), more box rotations but less box
offsets were achieved. In this condition, boxmobility
presented a wider range of distribution but a more
general deformed shape along the longitudinal
direction as shown in Figure 12. The highest forces
were measured in the boxes with upper bound native
soil strength, and the lowest forces were measured in
the boxes with Geofoam backfill.
4. Case 4 – Variation in the gap size: Case 4-A–Cwere
set up to promote maximum rotation with the
followingconditions: the fault is alignedat the quarter
point of the box, fault angle of 508 and high stiffnesscontrast between the native soil and the backfill
material. A large gap width results in large box
rotation but small offset. However, the net result is
similar in terms of rattle space as shown in Figure 13
(f). Different gap widths result in similar box-to-box
contact forces and normal forces acting on the boxes.
All analyses showed relatively low levels of vertical
segment movement and rotation in the lateral and
longitudinal axes of the vault. The rotations about the
vertical axis (on the horizontal plane) were significant but
still distributed only within one to two segments on either
side of the fault. Hence, the box rotations on the horizontal
plane are extremely important for the proper functioning
of the pipeline inside the vault. The deformation of the
vault on the horizontal plane was affected by the
following: (1) location of the fault as either centred on a
segment or centred on a connection joint and (2) nature of
the backfill between the vault and the secant pile wall.
The narrowest distribution of the segment movements
(combination of translation and rotation) from the fault
plane, which conforms to the most pronounced deformation
of the vault, occurred when the connection joint was centred
on the fault. The widest distribution of the segment
movements from the fault plane, which conforms to the
most gradual deformation of the vault, occurred when the
segment was located on the fault. The use of Geofoam as
backfill increased the maximum segment rotation and
broadened the distribution of the rotation compared with the
use of loose sand as backfill. Lastly, the variation in the
connection joint size in a narrow range has aminimal impact
on the mobility of the box in response to fault rupture.
The highest lateral pressure on the vault segments was
measured in cases where loose sand was placed between
the vault and the secant pile wall. The highest pressure
associated with the fault was approximately 30% of the
maximum horizontal passive pressure. The lowest
horizontal pressure was measured in cases where Geofoam
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was utilised as back fill. The pressure in these cases was
equal to or less than 10% of the maximum horizontal
passive pressure and less than 30% of the mobilised lateral
pressure when loose sand was placed between the vault
and the secant pile wall. The relatively low measured
pressure compared with the maximum passive limits
observed in the model simulation results from the secant
pile wall, which acts as a barrier between the vault and the
soil on the outboard side of the wall. During a fault
rupture, soil movement is resisted by the secant pile wall,
resulting in shear transfer between the soil and the intact
structural wall elements. This interaction between the
deformed soil and the secant pile wall reduces the pressure
transmitted to the vault to a relatively small fraction of the
maximum horizontal passive pressure.
8. Summary and conclusions
The seismic upgrade of BDPL 3 and 4 involves the
replacement of the existing BDPL 3 with a new BDPL 3X
enclosed in a segmental protective vault at its crossing of
the Hayward Fault. Numerical 3D model analyses were
Case 1A
Case 1B
Case 1C
Case 2A
Case 2B
Case 3A
Case 3B
Case 4A
Case 4B
Fault line
Case 4C
Figure 12. Final box positions at a 2.0-m fault displacement for the different cases.
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performed to simulate the complex protective vault system
when subjected to fault rupture. The analyses provide
information on the relative movement of the segments,
including rotation, relative offset and induced forces, and
thus enhances the understanding of the interaction among
the concrete vault, backfill and native soil.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
1-A 1-B 1-C 2-A 2-B 3-A 3-B 4-A 4-B 4-C
Rot
atio
n ab
out l
ongi
tudi
nal
axis
(de
gree
s)
(a)
1-A 1-B 1-C 2-A 2-B 3-A 3-B 4-A 4-B 4-C0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Rot
atio
n ab
out t
rans
vers
eax
is (
degr
ees)
(b)
1-A 1-B 1-C 2-A 2-B 3-A 3-B 4-A 4-B 4-C0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Rot
atio
n ab
out v
ertic
alax
is (
degr
ees)
(c)
1-A 1-B 1-C 2-A 2-B 3-A 3-B 4-A 4-B 4-C0.00
0.50
1.00
1.50
2.00
Box
offs
et (
m)
(d)
1-A 1-B 1-C 2-A 2-B 3-A 3-B 4-A 4-B 4-C0.0
5.0
10.0
15.0
20.0
Gap
wid
th (
cm)
(e)
1-A 1-B 1-C 2-A 2-B 3-A 3-B 4-A 4-B 4-C0
0.5
1
1.5
Rat
tle S
pace
(m
)
(f)
1-A 1-B 1-C 2-A 2-B 3-A 3-B 4-A 4-B 4-C0
2000
4000
6000
8000
10000
12000
Con
tact
forc
e (k
N)
(g)
1-A 1-B 1-C 2-A 2-B 3-A 3-B 4-A 4-B 4-C0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Nor
mal
ized
for
ce a
ctin
g on
box
es
(h)
Figure 13. Comparison of the output parameters at a 2.0-m fault displacement for the different cases.
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The influencing factors, such as fault location, fault
angle, fill material type and native soil condition were
studied. In response to a fault rupture in general, the
segmental vaults experienced rotation and translation as
rigid bodies. As a result, the connection joints between the
vaults partially closed as far as one to two segments from
either side of the fault. The compressive shortening of the
vault caused progressive closure of the connection joints,
which spread further from the fault as the strike-slip
displacement increased.
From the point of view of design, we recommend
designing the vault angle closer to the fault angle so that box
rotation as well as contact force can be minimised. The
analyses also demonstrated that connection joint size has a
minimal impact on system performance. Although a large
connection joint size results in more box rotation but less box
offset, the net result is similar in terms of rattle space at the
design fault movement. Lastly, Geofoam fill can significantly
reduce the earth pressure on the vault compared with sand fill
and leads to amoregradualdeformationalong the longitudinal
axis. Therefore, Geofoam is recommended for backfill.
Conclusively, the simulated vault deformation validated
the special design of rigid concrete segments with relatively
flexible connection joints oriented parallel to the strike of
the fault. After a design level of fault offset, the deformed
vault will leave enough rattle space for the pipeline to
accommodate the fault offset with slip and rotation joints.
Funding
This study was mainly conducted by the first author during hisemployment with URS Corporation and completed with fundingfrom the National Science Council [grant number NSC101-2218-E-005-005]. The authors gratefully acknowledge this support.
Notes
1. Email: philip.meymand@urs.com2. Email: ethan.dawson@urs.com3. Email: sawong@sfwater.org
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